Changesintheextracellular[K+]canhaveimportanteffectsonexcitablecells,especiallythoseoftheheart.Adecreaseinextracellular[K+](hypokalemia) hyperpolarizestheVmofcardiacmyocytesand,insodoing,makesinitiatinganactionpotentialmoredifficult,becausealargerdepolarizingcurrentisneededtoreachthreshold(see ).Ifsevere,hypokalemiacanleadtocardiacarrhythmias,andeventuallytheheartcanstopcontracting(asystole). Anincreaseintheextracellular[K+](hyperkalemia) canbeequallydeleterioustocardiacfunction.Withhyperkalemia,theVmisdepolarized,anditiseasiertoinitiateanactionpotential.However,oncetheactionpotentialfiresthechannelsbecomeinactivated,andareunabletoinitiateanotheractionpotential,untiltheyarereactivatedbynormalrepolarizationoftheVm.BecausetheVmisdepolarizedinhyperkalemia,thechannelsstayinaninactivatedstate.ThusdepolarizationoftheVmwithhyperkalemiacanleadtocardiacarrhythmiasandlossofcardiacmusclecontraction.
Eq. 2.7 also defines the limits for the membrane potential. In the example depicted in
Fig. 2.4, it is apparent that the Vm cannot be more negative than EK+ (−90.8 mV), as would be the case if the membrane were only conductive to K+ . Conversely, the Vm could not be more positive than ENa+ (66.6 mV); such a condition would be met if the membrane were conductive only to Na+ . The dependence of the Vm on the conductance of the membrane to specific ions is the basis by which action potentials in excitable cells are generated (
Fig. 2.5). As noted previously, in all excitable cells, the
CHAPTER 2 Homeostasis: Volume and Composition of Body Fluid Compartments membrane at rest is conductive predominantly to K+ , and thus Vm is near EK+. When an action potential is initiated, Na+-channels open and the membrane is now conductive predominantly to Na+ . As a result, Vm now approaches ENa+. The generation of action potentials is discussed in more detail in
TheestablishmentoftheVmrequirestheseparationofchargeacrosstheplasmamembrane.However,thenumberofionsthatmustmoveacrossthemembraneisatinyfractionofthetotalnumberofionsinthecell.Forexample,considerasphericalcellwithadiameterof20µmandaVmof−80mV.Furthermore,assumethatthisVmof−80mVistheresultofthediffusionofK+ outofthecellandthattheintracellular[K+]is120mmol/L.TheamountofK+ thatwouldhavetodiffuseoutofthecelltoestablishtheVmof−80mVisthencalculatedasfollows.
Firstthechargeseparationacrossthemembraneneedstobecalculated.Thisisdonewiththeknowledgethattheplasmamembranebehaveselectricallylikeacapacitor,thecapacitance(C)ofwhichisapproximately1µF/cm2,and whereQ= chargeandisexpressedinunitsofcoulombs.Ifthesurfaceareaofthecellis4πr2or1.26× 10−5cm2,thecapacitanceofthecelliscalculatedasfollows: 1× 10 F/cm × . × 10 cm = . × 10 126 126 F.
Thusthechargeseparationacrossthemembraneiscalculatedasfollows: 1 01× 10−12 coulombs.